1. Field of the Invention
The present invention relates generally to modelocking, and in particular, to cw modelocking in which Q-switched pulses are suppressed.
2. Description of the Related Art
Semiconductor saturable absorbers have recently found application in the field of passively modelocked, ultrashort pulse lasers. These devices are attractive since they are compact, inexpensive, and can be tailored to a wide range of laser wavelengths and pulsewidths. Semiconductor saturable absorbers were first used to passively modelock a diode laser (see P. W. Smith, Y. Silberberg and D. B. A. Miller, xe2x80x9cMode locking of semiconductor diode lasers using saturable excitonic nonlinearities,xe2x80x9d J. Opt. Soc. Am. B, vol. 2, pp. 1228-1236, 1985 and U.S. Pat. No. 4,435,809 to Tsang et al). Quantum well and bulk semiconductor saturable absorbers have also been used to modelock color center (M. N. Islam, E. R. Sunderman, C. E. Soccolich, I. Bar-Joseph, N. Sauer, and T. Y. Chang, xe2x80x9cColor center lasers passively mode-locked by quantum wellsxe2x80x9d, IEEE J. of Quantum Electronics, vol. 25, pp. 2454-2462 (1989)) and fiber lasers (U.S. Pat. No. 5,436,925 to Lin et al.).
A saturable absorber has an intensity-dependent loss l. The single pass loss of a signal of intensity I through a saturable absorber of thickness d may be expressed as
l=1xe2x88x92exp(xe2x88x92xcex1d)xe2x80x83xe2x80x83(1)
in which xcex1 is the intensity dependent absorption coefficient given by:
xcex1(I)=xcex10/(1+I/ISAT)xe2x80x83xe2x80x83(2)
Here xcex10 is the small signal absorption coefficient, which depends upon the material in question. ISAT is the saturation intensity, which is inversely proportional to the lifetime (xcfx84A) of the absorbing species within the saturable absorber. Thus, saturable absorbers exhibit less loss at higher intensity.
Because the loss of a saturable absorber is intensity dependent, the pulse width of the laser pulses is shortened as they pass through the saturable absorber. How rapidly the pulse width of the laser pulses is shortened is proportional to |dq0/dI|, in which q0 is the nonlinear loss:
q0=l(I)xe2x88x92l(I=0)xe2x80x83xe2x80x83(3)
l(I=0) is a constant (=1xe2x88x92exp(xe2x88x92xcex10d)) and is known as the insertion loss. As defined herein, the nonlinear loss q0 of a saturable absorber decreases (becomes more negative) with increasing intensity I. |dq0dI| stays essentially constant until I approaches ISAT, becoming essentially zero in the bleaching regime, i.e., when I greater than  greater than ISAT.
For a saturable absorber to function satisfactorily as a modelocking element, it should have a lifetime (i.e., the lifetime of the upper state of the absorbing species), insertion loss l(I=0), and nonlinear loss q0 appropriate to the laser. Ideally, the insertion loss should be low to enhance the laser""s efficiency, whereas the lifetime and the nonlinear loss q0 should permit self-starting and stable cw modelocking. The saturable absorber""s characteristics, as well as laser cavity parameters such as output coupling fraction, residual loss, and lifetime of the gain medium, all play a role in the evolution of a laser from startup to modelocking.
To obtain rapid pulse shortening in a self-starting cw modelocked laser having a saturable absorber, the intensity on the saturable absorber should be high and the absorber should have a nonlinear loss q0 whose magnitude is large. On the other hand, reducing the loss of the saturable absorber causes the intracavity power to increase, which may lead to gain saturation. If the gain saturation does not dampen power increases caused by the large magnitude of the nonlinear loss q0, the laser will operate in a regime in which the laser Q-switches and modelocks simultaneously (see H. A. Haus, xe2x80x9cParameter range for cw passive mode locking,xe2x80x9d IEEE, J. Quantum Electronics, QE-12, p. 169, 1976). This is particularly true for a laser medium with a very long lifetime such as an erbium-doped. fiber (xcfx84xcx9cms). Thus, to avoid Q-switching, the magnitude of the nonlinear loss q0 of the saturable absorber must be limited, but not to the point where self-starting of the modelocking becomes difficult. The insertion loss and the nonlinear loss q0 of a semiconductor saturable absorber can be controlled by selecting a material having the appropriate band gap and thickness.
The loss characteristics of a simple saturable absorber may be modified by the Fabry-Perot interference effect. Indeed, semiconductor saturable absorbers tend to form a natural Fabry-Perot structure since a semiconductor""s relatively high index of refraction (typically 2-4) results in a semiconductor-air interface from which xcx9c10-40% of the incident light may be reflected. A semiconductor saturable absorber may have one side that is high reflection coated (e.g., for maximum reflectivity), with this high reflector forming one end of a laser cavity. In this case, the fraction RF-P of the intracavity power that is reflected from the semiconductor saturable absorber is given by
RF-P=1xe2x88x92(1xe2x88x92R)(1xe2x88x92T)[1+RT+2(RT)1/2 cos(2xcex4)]xe2x88x921xe2x80x83xe2x80x83(4)
in which R is the front surface reflectivity of the saturable absorber (i.e., the reflectivity of the saturable absorber and any reflection coating thereon in the absence of reflection from the back side), xcex4=(2nd/xcex)2xcfx80 is the double pass phase change, d is the sample thickness, n is the index of refraction, and xcex is the wavelength of interest. T is the double pass transmission through the saturable absorber and is equal to exp(xe2x88x922xcex1d), with xcex1 being the absorption coefficient of the material. The corresponding absorption is then A=1xe2x88x92T=1xe2x88x92exp(xe2x88x922xcex1d). If multiple layers with different indices of refraction and absorption coefficients are used as part of the Fabry-Perot etalon, equation (4) must be modified so that the double pass phase change and the absorption are summed over all the layers.
The fraction of the laser cavity power incident on the Fabry-Perot structure that is absorbed in the saturable absorber (FABS) is in general not simply 1xe2x88x92T, but rather 1xe2x88x92RF-P. This is due to the fact that a Fabry-Perot structure acts as a resonating structure, in which power may circulate before reentering the rest of the laser cavity.
According to equation (4), RF-P (the fraction of the intracavity standing power reflected from a semiconductor saturable absorber) is a sensitive function of the double pass phase change xcex4, which depends upon the laser wavelength as well as the thickness and index of refraction of the saturable absorber. As illustrated in FIG. 1, for a given laser wavelength xcex and index of refraction n, the reflectivity of a Fabry-Perot device is a periodic function that depends upon the thickness d of the saturable absorber. If the thickness of the Fabry-Perot device is chosen to be d=xcexm/2n, in which m is a positive integer, the double pass phase change is xcex4=2mxcfx80, and the Fabry-Perot device is said to be at antiresonance. In this case, RF-P=1xe2x88x92(1xe2x88x92R)(1xe2x88x92T)[1+(RT)1/2]xe2x88x922.
In addition to wavelength and thickness, RF-P can also be viewed as a function of R. FIG. 2 considers how RF-P varies as a function of R and wavelength xcex for a given saturable absorber thickness d. In particular, the higher R is, the more rapidly RF-P varies. When R=0 (i.e., when the surface of the saturable absorber that faces the gain medium is anti-reflection coated), RF-P=T and thus depends solely upon the absorption of the saturable absorber. For a Fabry-Perot intracavity saturable absorber with a highly reflecting back surface such as that considered here, it is often desirable to avoid the xe2x80x9cetaloningxe2x80x9d effect altogether by anti-reflection coating the surface facing the gain medium.
In general, however, Rxe2x89xa00, and by choosing d and R appropriately, the loss of a Fabry-Perot saturable absorber can be effectively controlled. If the thickness of the saturable absorber is chosen to be a multiple integer of       λ          2      ⁢      n        ,
the device is said to be an anti-resonant Fabry-Perot saturable absorber (A-FPSA) see U. Keller et al., xe2x80x9cSolid-state low-loss intracavity saturable absorber for Nd:YLF lasers: an antiresonant semiconductor Fabry-Perot saturable absorber,xe2x80x9d Opt. Lett., vol. 17, p. 505, 1992 and U.S. Pat. No. 5,237,577 to Keller et al.) In an A-FPSA, the side of the device facing the gain medium usually includes a high reflector. In this configuration, most of the incident light is reflected from the gain-medium-facing surface and little goes into the saturable absorber, thus reducing the light absorbed by the saturable absorber. This low absorption design is appropriate for lasers with small output coupling and low single pass gain, such as solid state lasers. For example, if the laser has an output coupler of xcx9c4%, an insertion loss of nearly 0.5% may be desirable, which is lower than what is normally obtained from either a quantum well or bulk absorber semiconductor. Low loss A-FPSA devices have been used successfully in modelocked solid-state lasers (see, for example, U. Keller, D. A. B. Miller, G. D. Boyd, T. H. Chiu, J. F. Ferguson, and M. T. Asom, xe2x80x9cSolid-state low-loss intracavity saturable absorber for Nd:YLF lasers: an antiresonant semiconductor Fabry-Perot saturable absorber,xe2x80x9d Opt. Lett., 17, 505, 1992).
Other low loss designs have been successfully used in modelocking arrangements. For example, a quantum well saturable absorber can be inserted into a Semiconductor Bragg Reflector (SBR) (see U.S. Pat. No. 5,627,854 to Knox and also S. Tsuda, W. H. Knox, E. A. de Souza, W. Y. Jan, and J. E. Cunningham, xe2x80x9cLow-loss intracavity AlAs/AlGaAs saturable Bragg reflector for femto-second mode locking in solid state lasers,xe2x80x9d Opt. Lett., vol. 20, p. 1406, 1995). In this arrangement, light intensity decreases rapidly inside the SBR, and the insertion loss is controlled by precisely placing absorbing layers within the SBR.
Another means of manipulating the effective insertion and nonlinear losses is through appropriate positioning of the absorber in a standing wave. In this design, an incident beam is reflected by a high or partial reflector to form an intracavity standing wave in which the intensity varies between zero and twice the incident intensity. The insertion and nonlinear losses are controlled by appropriate positioning of absorbing layers within the standing wave electric field. In U.S. Pat. No. 5,701,327 to Cunningham et al., the quantum well absorption layers are inserted into a multiple half wavelength thick strain relief layer which is then deposited on top of an SBR Since the total thickness of the strain relief layer is a multiple integer of half wavelengths a standing wave node is formed (where the intensity is minimum) at the surface facing the incident beam. This antiresonant design limits the amount of light going into the strain relief layer and hence limits the amplitude of the standing wave.
In another design (see U.S. Pat. No. 4,860,296 to Chemla et al.), nonlinear loss is maximized by placing thin absorbing layers (separated by transparent spacers) at the antinodes of a standing wave to form a so called grating saturable absorber. By placing the absorbing layers at the antinodes, where the intensity is twice the average value, the nonlinear loss can be enhanced by up to a factor of 2 if the absorbing layers are very thin compared to the transparent spacers.
All of these prior art designs involve saturable absorbers having low insertion loss. Accordingly, the magnitude of the nonlinear loss is limited, being maximized when the saturable absorber is completely bleached. For a high gain, high output fiber laser, however, the magnitude of the nonlinear loss is preferably large for modelocking to be self-starting. On the other hand, the use of a highly nonlinear saturable absorber may lead to persistent Q-switching. Thus, there remains a need for saturable absorbers suitable for self-starting modelocking of high gain, high output lasers such as fiber lasers.
The method of achieving self-starting cw mode-locking evolving from Q-switched mode-locking (QSML) is disclosed. In contrast, the modelocking of most solid state lasers begins from cw noise.
The use of interactivity Resonant Fabry-perot Absorbers (R-FPSA) for inducing self-starting mode-locking in a laser is also disclosed. An optical power limiter such as a two photon absorber (TPA), e.g., a semiconductor material, is optionally used in the laser cavity to inhibit Q-switching. The R-FPSA is designed such that the nonlinear loss experienced by the saturable absorber is enhanced over the prior art A-FPSA configurations. The TPA power limiter provides effective damage protection for the R-FPSA and self-adjusts the total nonlinear loss of the laser to be in the stable cw mode-locking region.
The R-FPSA includes two reflectors having a spacing of roughly (2m+1)xcex/4n. One reflector is preferably a maximum reflector that defines one end of the laser cavity (the xe2x80x9cend reflectorxe2x80x9d), whereas the other reflector is formed by a high or partial reflector that faces the gain medium of the laser (the xe2x80x9cinner reflectorxe2x80x9d).
When the Fabry-Perot device has a thickness given by nd=(2m+1)xcex/4, the double pass phase change is xcex4=(2m+1)xcfx80, and the Fabry-Perot structure is said to be at resonance. In this case, RF-P=1xe2x88x92(1xe2x88x92R)(1xe2x88x92T)[1xe2x88x92(RT)1/2]xe2x88x922 and is a minimum. By operating at resonance, the laser intensity absorbed by the saturable absorber is enhanced. The absorbed intensity for the R-FPSA is given by IAbs=(1xe2x88x92RF-P)I=(1xe2x88x92T)(1xe2x88x92R)/[1xe2x88x92(RT)1/2]2I, as can be determined from equation (4) with cos(2xcex4)=xe2x88x921. This is to be compared with the case in which the front surface is anti-reflection coated (R=0) and IABS=(1xe2x88x92T)I. Thus, by operating the Fabry-Perot device at resonance, the intensity absorbed by the saturable absorber is increased by a factor of (1xe2x88x92R)/[1xe2x88x92(RT)1/2]2.
The effect of varying R on RF-P(xcex) for an R-FPSA is illustrated in FIG. 2. The spacing between adjacent minima is given by xcex94xcex=xcexm+1xe2x88x92xcexm=xcexm xcexm+1/2nd and is preferably large for certain applications such as ultrafast lasers, where broad bandwidth is needed. The inner reflector should have a reflectivity R sufficiently high to provide a desired intensity on the saturable absorber. This reflectivity R, however, should not be so high that RF-P(xcex) is no longer relatively flat over the gain profile. For example, if the inner reflector reflectivity R is too high, the bandwidth of RF-P(xcex) at resonance needed for modelocked laser pulses may be too limited. For applications in which the spot size on the saturable absorber can not be varied (e.g., butt-coupling to a fiber or a waveguide), xe2x80x9ctuningxe2x80x9d the intensity on the absorber by selecting an appropriate R may be desirable.
The resonant effect on the nonlinear loss and RF-P as a function of wavelength is explored in FIG. 3. This figure shows that the nonlinear loss experiences a significant enhancement when the Fabry-Perot device is designed to be at resonance. The negative nonlinear loss is calculated asxe2x80x94q=RF-P(R,T)xe2x88x92RF-P(R,T0). Where T=exp(xe2x88x922xcex1d)=T0exp(xe2x88x922(xcex4xcex1)d)xcx9cT0(1xe2x88x922(xcex4xcex1)d), with T=exp(xe2x88x922xcex10d)=50% and 2(xcex4xcex1)d approximated as 0.2(1xe2x88x92RF-P), proportional with the light absorbed in the sample. It can be seen that, the nonlinear loss at resonant (near 1540 nm) is 7 times larger than that at anti-resonant.
In one preferred embodiment, the gain medium is an erbium doped fiber having an upper state lifetime on the order of milliseconds (ms), and the round trip cavity time is typically 10-100 nsec. By using an R-FPSA with a large nonlinear loss, the fiber laser may operate in a QSML regime rather than a cw modelocked regime. In this case, it may be necessary to suppress the intense Q-switched pulses, thereby driving the laser below threshold. In a preferred embodiment of this invention, a two photon absorber (TPA) is used for this purpose to complement the R-FPSA, so that the laser operates in a cw modelocked regime. The TPA preferably has little or no single photon absorption at the laser wavelength. Thus, two different types of absorbers, having different nonlinear behavior, may be used in the same device to achieve self-starting, cw modelocked behavior.
The different intensity dependencies of a preferred saturable absorber (InGaAsP) and a preferred two photon absorber (InP) are illustrated in FIG. 4. The loss due to the two photon absorber increases strongly as a function of intensity, whereas the loss due to the saturable absorber decreases (saturates) with increasing intensity. The resultant xe2x80x9cV-shapedxe2x80x9d total loss of FIG. 4 has a minimum which is a favorable regime for cw modelocking.
The optical limiter (e.g., the TPA) preferably has a large two photon absorption coefficient xcex22, which is a function of the ratio of the material""s band gap Eg and the photon energy,   h      2    ⁢    π  
see, for example, E. W. Van Stryland, M. A. Woodall, H. Vanherzeele, and M. J. Soileau, xe2x80x9cEnergy band-gap dependence of two-photon absorption,xe2x80x9d Opt. Lett., 10, 490, 1985). FIG. 5 shows how the two photon coefficient scales with this ratio, which is given by (Stryland et al., supra):       β    2    =                    κ        ⁡                  [                                                                      (                                                                                    h                        /                                                  E                          g                                                                    -                      1                                        )                                    )                                                  3                  /                  2                                                            2                ⁢                π                                      /                                          (                                                      h                    /                                          E                      g                                                                            2                    ⁢                    π                                                  )                            5                                ]                    /              n        2              ⁢          E      g      
Here xcexa is a nearly material independent parameter. For a given laser wavelength, the band gap Eg of the optical power limiter should be larger than the photon energy       h          2      ⁢      π        ,
so that maximum two photon absorption can be obtained without significant increase in the insertion loss. The band gap can be easily controlled by proper choice of the semiconductor material and/or its doping levels.
The TPA is effective at suppressing QSML regardless of its position in the laser cavity. For example, the TPA may adjoin the saturable absorber. Alternatively, the TPA and the saturable absorber may be located on opposite sides of the gain medium, or several TPAs may be used to reduce the thickness of the Fabry-Perot device, thereby offering greater design flexibility (in accordance with equation (4)).
Suppression of Q-switched pulses by two photon absorbers has been previously reported (see, for example, A. Hordvik, xe2x80x9cPulse stretching utilizing two-photon-induced light absorptionxe2x80x9d, J. of Quantum Electronics, QE-6, 199 (1970) and V. A. Arsen""ev, I. N. Matveev, and N. D. Ustinov, xe2x80x9cNanosecond and microsecond pulse generation in solid-state lasers (review)xe2x80x9d, Sov. J. Quantum Electron, vol. 7 (11), 1321 (1978)). Also, semiconductor-based two photon absorbers have been used as optical power limiters to protect damage sensitive optics (see, for example, U.S. Pat. No. 4,846,561 to Soileau et al.).
The band gap of a two photon absorber lies well above the photon energy at the laser wavelength, so that single photon absorption is low at low intensities. At higher intensities, however, the production rate of carriers generated from the valance band to the conduction band increases. The absorption (1xe2x88x92T) from two photon effects is given by:
xe2x80x83ATPA=xcex22IdTPA/(1+xcex22IdTPA)xe2x80x83xe2x80x83(6)
where dTPA is the thickness of the TPA material and xcex22 is the TPA coefficient. (See, for example, E. W. Van Stryland, H. Vanherzeele, M. A. Woodall, M. J. Soileau, A. Smirl, S. Guha, and T. F. Boggess, xe2x80x9cTwo photon absorption, nonlinear refraction, and optical limiting in semiconductorsxe2x80x9d, Opt. Engin., vol. 24, 613, 1985).
A two photon absorber tends to limit the pulse shortening of high intensity pulses, since pulse peaks are more strongly attenuated than the wings. Thus, the conventional understanding of the two photon absorption effect is that it degrades the performance of modelocked lasers (see, for example, A. T. Obeidat and W. H. Knox, xe2x80x9cEffects of two-photon absorption in saturable Bragg reflectors in femtosecond solid-state lasersxe2x80x9d, OSA Technical Digest, 11, 130, Proceedings of CLEO"" 97). In the high gain fiber laser disclosed herein, however, Q-switched modelocking is the main impediment to cw modelocking. Thus, the two photon absorber effectively suppresses QSML, thereby facilitating cw modelocking, which is not significantly affected by the two photon absorber. The result is that the intracavity use of one or more two photon absorbers permits a wider range of saturable absorbers to be used.
The combination of the R-FPSA and the TPA optical limiter disclosed herein provides an ideal nonlinear device for self-starting modelocking, since the R-FPSA provides quick pulse shortening due to its large saturable loss, and the optical limiter self adjusts the nonlinear loss to be within the cw modelocking stability region (FIG. 4). The TPA power limiter also provides effective damage protection for the saturable absorber. The intensity on the saturable absorber can be optimized by varying the spot size on the absorber, or by selecting R appropriately.